Remember that distance equals speed times time: [tex]d=st[/tex]. We know for our problem that the speed of our first jet is 377 mph, so [tex]s_{1}=377[/tex]. We also know the speed of our second one is 275 mph, so [tex]s_{2}=275[/tex]. Since the the time that will it take for the jets to be 9128 miles apart is the same, [tex]t[/tex] is going to be equal for both jets. Now we can setup our distance equations for both jets.
For our first jet:
[tex]d_{1}=377t[/tex]
For our second jet:
[tex]d_{2}=275t[/tex]
We know for our problem that after [tex]t[/tex] the jets will be 9128 miles apart, so the total distance will be 9128: [tex]d_{t}=9128[/tex]. Since our jets are traveling in opposite directions, the distance between them will increase over time, so we are going to add [tex]d_{1}[/tex] and [tex]d_{2}[/tex], and set them equal to [tex]d_{t}[/tex] to find our time:
[tex]d_{t}=d_{1}+d_{2}[/tex]
[tex]9128=377t+275t[/tex]
[tex]9128=652t[/tex]
[tex]t= \frac{9128}{652} [/tex]
[tex]t=14[/tex]
We can conclude that our jets will be 9128 miles apart after 14 hours.
